Multivariate Analysis of Genetic Diversity of Bolivian Quinoa Germplasm

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Multivariate Analysis of Genetic Diversity of BolivianQuinoa GermplasmWilfredo Rojas aa Fundación PROINPA , La Paz, BoliviaPublished online: 18 Aug 2006.

To cite this article: Wilfredo Rojas (2003) Multivariate Analysis of Genetic Diversity of Bolivian Quinoa Germplasm, FoodReviews International, 19:1-2, 9-23, DOI: 10.1081/FRI-120018864

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Multivariate Analysis of Genetic Diversity ofBolivian Quinoa Germplasm

Wilfredo Rojas*

Fundacion PROINPA, La Paz, Bolivia

ABSTRACT

To determine the genetic diversity of quinoa (Chenopodium quinoa Willd.), the crop’s

morphological traits and agronomic performance were evaluated during 1992–1993

and 1993–1994, using germplasm preserved in Bolivia and IBPGR descriptors as

modified by the Fundacion PROINPA’s Quinoa Project. Three multivariate methods

were used to analyze diversity, allowing sets of individuals to be described and

grouped, while considering multiple characteristics and their interrelationships.

Principal component analysis was used to quantify the contribution of the three

components most associated with total variance, and to identify the variables

characterizing each of these components. The nonhierarchical procedure (k-means) of

cluster analysis was used to group accessions according to genetic diversity. The

resulting seven clusters were combined with passport data to provide useful

descriptions of the germplasm. Multiple discriminatory analysis complemented the

study, deriving, through the step-by-step procedure, six statistically significant ðP ¼

0:001Þ functions. The discriminatory ability of each independent variable was

quantified through the index of potency. About 92% of the accessions were readily

classified into the seven groups identified by cluster analysis. The Mahalanobis

distance (D 2) method was used to show their statistical differences. Even incorrectly

classified accessions were identified and reassigned to a more appropriate group.

Key Words: Andean crop; Quinoa; Genetic variability; Germplasm; Multivariate

methods.

9

DOI: 10.1081/FRI-120018864 8755-9129 (Print); 1525-6103 (Online)

Copyright q 2003 by Marcel Dekker, Inc. www.dekker.com

*Correspondence: Wilfredo Rojas, Fundacion PROINPA, La Paz, Bolivia; E-mail: quinualp@

mail.megalink.com.

FOOD REVIEWS INTERNATIONALVol. 19, Nos. 1 & 2, pp. 9–23, 2003

MARCEL DEKKER, INC. • 270 MADISON AVENUE • NEW YORK, NY 10016

©2003 Marcel Dekker, Inc. All rights reserved. This material may not be used or reproduced in any form without the express written permission of Marcel Dekker, Inc.

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INTRODUCTION

Andean crops characteristically have broad genetic variability. However, in many

species, this variability is not adequately used in genetic breeding programs, because it has

not been specifically defined and the potential applications are unknown. One such crop is

quinoa (Chenopodium quinoa Willd.), with edible starchy seeds that have a high potential

in the fresh-food market.

Bolivia has a collection of over 2500 quinoa accessions, including entries from the

Andes between Ecuador and northwestern Argentina and from the coastal lowlands of

Chile.

In order to provide important alternative applications that help promote the crop’s use

as well as guidelines for future collections, plant breeders must understand the patterns of

variability and grouping of quinoa germplasm. Maintaining this crop’s broad variability is

crucial for its stability in Bolivia and in most of the Andean region.

Toward this end, three multivariate methods were applied (Dillon and Goldstein,

1984; Hair et al., 1992) to describe and group sets of individual quinoa accessions,

simultaneously taking into account several characteristics and the relationships between

them. The study aimed to determine patterns of germplasm variation and to identify and

classify groups of accessions with different genetic diversity.

MATERIALS AND METHODS

Of the entire quinoa germplasm collection, 1512 accessions were analyzed for their

diversity. Most of the accessions were Bolivian and Peruvian, but entries from Argentina

and Chile were also included (Table 1). The geographic range of the accessions was from

118S in Peru to 438S in southern Chile. Altitudes ranged between sea level (Chile) and

3885 meters above sea level (masl) (Bolivia).

Table 1. Number of accessions and origin of quinoa germplasm included in the

analysis of the crop’s genetic diversity.

Country of origin

Department

or region

Number of

accessions Subtotal

Bolivia La Paz 300

Oruro 412

Potosı 176

Cochabamba 68

Chuquisaca 72

Tarija 15 1043

Peru Puno 423

Cusco 22 445

Chile Southern 12 12

Argentina Northern 12 12

Total 1512

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Germplasm characterization and agronomic evaluation were performed during 1992–

1993 and 1993–1994 at the Patacamaya Experiment Station, located in the High Plains,

Department of La Paz, Bolivia (178150S, 688550W; 3789 masl). Climate varies from arid to

semiarid, the average annual precipitation is 381 mm, the average annual temperature is

118C, and the average number of frost-days per year is 187.

Quantitative variables considered in the descriptive and multivariate analyses were

phenological (emergence of seedlings and flower buds, initiation of flowering, 50%

flowering, and physiological maturity); and morphological (number of branches, number

of teeth on the serrated margins of leaves, stem diameter, panicle length, panicle diameter,

and plant height), related to the grain (grain diameter, weight of 100 grains, and saponin

content) and the harvest index. Two qualitative variables—panicle shape and growth

habit—were included as supplementary or illustrative data for cluster analysis.

STATISTICAL ANALYSIS

Central trend and dispersion descriptive analyses were applied to estimate and

describe the performance of the different accessions in terms of each character (Steel and

Torrie, 1988).

The analysis of genetic diversity was performed with SYSTAT program, version 5

(Wilkinson, 1988), following four steps:

1. Estimation of the degree of association among the different characteristics

analyzed, according to Pearson’s coefficient (Clifford and Stephenson, 1975).

2. Derivation of orthogonal variables, using principal components analysis (Dillon

and Goldstein, 1984).

3. Classification of accessions in similar groups by either the nonhierarchical

procedure or k-means technique of cluster analysis (Hair et al., 1992).

4. Verification of the significance between groups by multiple discriminatory

analysis, reclassifying each group and determining the discriminatory power of

each variable (Dillon and Goldstein, 1984; Hair et al., 1992).

RESULTS

Descriptive Statistical Parameters

Table 2 summarizes the parameters estimated for each quantitative variable. Initiation

of flowering, 50% flowering, and physiological maturity were the more important

phenological variables according to their dispersion in relation to the mean. The earliest

maturing accessions reached maturity in 119 days, and the latest in 209 days, with a

3-month interval between the earliest- and the latest-maturing quinoa accessions. This

broad variability is promising from the viewpoint of genetic improvement to cope with

abiotic problems such as frost and drought, the two factors that most affect crop production.

Harvest index also presented broad variability. Accessions with low harvest

indexes, depending on plant architecture, can become forage alternatives, whereas quinoa

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accessions with high harvest indexes can be used for grain production. In addition, the

significant variations in grain diameter, weight of 100 grains, and saponin content can be

used to improve product market presentation. Plants with highly diverse architecture can

be used according to the breeding objectives pursued.

Pearson’s Coefficient

Of all coefficients, 83 were highly significant ðP # 0:001Þ: However, coefficients

higher than 0.4 were considered as linear associations representing natural variation

patterns. The most important correlations, therefore, corresponded to variables related to

phenology and the grain, rather than to morphology.

Among the phenological variables, the highest correlation corresponded to initiation

of flowering and 50% flowering ðr ¼ 0:94Þ: Traits presenting highly significant

correlations with these two characteristics were flower buds, with r ¼ 0:69 and r ¼

0:73; respectively; physiological maturity, with r ¼ 0:63 and r ¼ 0:61; and harvest index,

with r ¼ 20:59 and r ¼ 20:57: The negative correlations with the harvest index show

that these values tend to become smaller as the phenological phase continues. This

phenomenon is corroborated by the negative correlations with physiological maturity

ðr ¼ 20:55Þ and flower buds ðr ¼ 20:42Þ:The positive correlations between physiological maturity and plant height ðr ¼ 0:56Þ

and stem diameter ðr ¼ 0:41Þ indicate that plants tend to become taller and their stems

thicker the longer the phenological cycle. However, the negative correlation formed with

weight of 100 grains ðr ¼ 20:42Þ indicates that, in turn, harvest indexes become lower.

Table 2. Statistical parameters of central trend and dispersion for quantitative characteristics.

Characteristics Range of variation Average SDa CVb (%)

Emergence (days) 8.00–21.00 13.13 1.96 14.93

Flower buds (days) 38.00–95.00 51.72 5.66 10.94

Initiation of flowering (days) 50.00–121.00 79.69 10.20 12.80

50% flowering (days) 60.00–145.00 93.50 12.04 12.88

Physiological maturity (days) 119.00–209.00 176.89 19.79 11.19

Harvest index 0.06–0.87 0.40 0.12 30.00

Main branches (no.) 0.00–42.20 21.36 6.36 29.77

Teeth on leaf margins (no.) 4.80–43.00 14.61 4.74 32.44

Stem diameter (mm) 10.16–26.26 17.12 2.66 15.54

Panicle length (cm) 15.40–62.80 37.41 8.09 21.62

Panicle diameter (cm) 2.86–19.42 6.85 1.66 24.23

Plant height (cm) 54.00–174.20 110.84 17.51 15.80

Grain diameter (mm) 1.36–2.66 1.96 0.23 11.73

Weight of 100 grains (g) 0.12–0.60 0.27 0.08 29.63

Saponin content (cc) 0.00–10.88 3.16 3.02 95.57

a SD ¼ standard deviation.b CV ¼ coefficient of variation.

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Risi and Galwey (1989b) also reported significant associations for physiological maturity

and stem diameter, as did Ochoa and Peralta (1988) for physiological maturity and weight

of 100 grains.

Positive associations between 50% flowering and number of branches ðr ¼ 0:44Þ and

number of teeth on leaf margins ðr ¼ 0:45Þ; and between initiation of flowering and

number of branches ðr ¼ 0:43Þ indicate that those accessions that flower late develop more

branches and leaves that are more dentated, as was evident in the accessions from the

valleys. Risi and Galwey (1989b) had similar results for these characteristics.

Grain diameter and weight of 100 grains formed the second most important

correlation ðr ¼ 0:89Þ: Grain diameter also correlated positively with saponin content

ðr ¼ 0:40Þ and negatively with panicle length ðr ¼ 20:40Þ; indicating that large-grained

accessions tend to develop short panicles and high saponin content. Cayoja (1996) and

Ochoa and Peralta (1988), in similar evaluations of quinoa germplasm, also determined

highly significant correlations for grain diameter and weight of 100 grains.

Among morphological variables, stem diameter correlated positively with plant

height ðr ¼ 0:69Þ; panicle diameter ðr ¼ 0:60Þ; and panicle length ðr ¼ 0:40Þ; and panicle

length correlated positively with plant height ðr ¼ 0:58Þ; indicating that accessions with

greater stem diameters and plant height during early phenological phases also developed

larger panicles. Risi and Galwey (1989b) determined that plant height, stem diameter, and

panicle length and diameter were significantly correlated with each other. Ochoa and

Peralta (1988) also found associations of panicle length with stem diameter and plant

height.

Principal Components Analysis

This analysis clearly and concisely explained the genetic diversity of quinoa. The

linear transformation performed by this method generated a new set of 15 independent

variables, known as principal components, that expressed results in their proper values and

vectors (Table 3). Proper values measure the importance and contribution of each

component to total variance, whereas each coefficient of proper vectors indicates the

degree of contribution of every original variable with which each principal component is

associated. The higher the coefficients, regardless of the sign, the more effective they will

be in discriminating between accessions.

There are no inferential tests to prove significance of proper values. Therefore, we

chose to follow the criterion established by Kaiser (1960), which adapts well to the

purpose of this analysis. This criterion is based on the selection of those components with a

proper value of 1. According to this criterion, the first three components account for more

than 63% of total variation (Table 3), giving a clear idea of the structure underlying the

quantitative variables analyzed.

The first principal component accounted for more than 30% of total variance, whereas

initiation of flowering, 50% flowering, and physiological maturity were the variables that

contributed most positively. In contrast, the variable contributing most negatively was the

harvest index with respect to grain diameter and weight of 100 grains (Table 3).

As a result, the first component differentiated those accessions that flower and mature

later in the season and thus, register low harvest index values from those with opposite

characteristics. The positive contribution of plant height and stem diameter indicates that




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these accessions, in addition to being late-maturing, develop prominent plant architectures

that negatively affect the harvest index, although the negative signs of grain diameter and

weight of 100 grains indicate that low harvest indexes are also partly a result of the

formation of small grains. In addition, these accessions are characterized by having many

teeth on their leaves and greater branching.

Except for seedling emergence, the first component identified mainly phenological

variables, denoting a clear delimitation and positive contribution of phases, and, in the

contrary sense, of harvest index, even though both plant height and stem diameter were

important and discriminatory. Scaff (1996) observed similar performance for phenological

variables when he studied the diversity of accessions collected in southern Chile. Risi and

Galwey (1989a) had different results for this component, except for seedling emergence,

which presented a negative contribution. In contrast, phenological variables were

important for the second component, with the difference, however, that these variables

were considered independently.

The second principal component accounted for more than 21% of total variance.

Variables highly and positively correlated were grain diameter and weight of 100 grains,

followed by saponin content. In contrast, most morphological variables presented a

negative, secondary contribution, although panicle length had the highest negative

coefficient value (20.785) (Table 3). Consequently, this component distinguished those

quinoa accessions forming large grains, with high saponin content and small plant

architecture in terms of plant height, stem diameter, and panicle size.

The second component thus identified grain-related variables presenting positive

contributions and, secondarily, morphological variables that contributed in both

senses. Harvest index and phenological variables, except flower buds, were not important.

Table 3. Coefficient values and vectors associated with the first three principal components.

Principal components First Second Third

Proper values 4.535 3.157 1.835

Percentage variance 30.235 21.045 12.235

Coefficient vector

Emergence (days) 0.294 20.228 20.123

Flower bud (days) 0.631 0.466 20.255

Initiation of flowering (days) 0.851 0.298 20.208

50% flowering (days) 0.849 0.346 20.184

Physiological maturity (days) 0.813 20.223 20.114

Harvest index 20.686 20.176 0.141

Main branches (no.) 0.471 0.393 0.352

Teeth on leaf margins (no.) 0.438 0.451 0.017

Stem diameter (mm) 0.588 20.346 0.560

Panicle length (cm) 0.178 20.785 0.238

Panicle diameter (cm) 0.279 20.308 0.648

Plant height (cm) 0.623 20.418 0.420

Grain diameter (mm) 20.282 0.711 0.488

Weight of 100 grains (g) 20.35 0.672 0.462

Saponin content (cc) 0.065 0.527 0.320

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Riveros (1997) likewise found that grain diameter and weight of 100 grains were the

variables that contributed most to this component, highlighting the limited relationship

with phenological variables. On the contrary, Risi and Galwey (1989a) found that all

phenological variables except seedling emergence were the most important, even though

correlations were negative. Of the morphological variables, panicle diameter had the

highest coefficient.

The third principal component (12%) was associated with panicle and stem diameters,

plant height, grain diameter, and weight of 100 grains, thus differentiating those

accessions with outstanding architecture, plant height, thick stems, large panicles, and

medium to large grains (Table 3). Scaff (1996) found that stem diameter and plant height

were the variables that contributed most, whereas Risi and Galwey (1989a) and Riveros

(1997) found that panicle length was the most significant.

The proportion of variance was quantified for each original variable in terms of three

components selected to determine the degree of importance (Table 4). Phenological

variables, except for seedling emergence, were more important than grain-related

variables, and these, in turn, were more important than morphological variables. Among

the first group (phenological variables), 50% flowering and initiation of flowering were

outstanding, followed by physiological maturity; in the second group, grain diameter and

weight of 100 grains; and in the third group, stem diameter and plant height.

Harvest index, despite its important contribution to the first component, occupied a

relatively low position, contributing insignificantly to the other two components. The

contributions of the variables (number of teeth on leaf margins and saponin content) to the

third and first components, respectively, were also insignificant. Of all the variables

studied, seedling emergence was the least discriminatory (Table 4).

Table 4. Degree of importance of quantitative variables as determined by the potency index

(for the multiple discriminatory analysis) and the proportion of variance (for the principal

component analysis).

Characteristic name Abbreviation

Potency

index Characteristics

Proportion of

variance

50% flowering (F50%) 0.234 F50% 0.875

Physiological maturity (PM) 0.178 IF 0.856

Grain diameter (GD) 0.169 GD 0.824

Weight of 100 grains (W100) 0.16 W100 0.788

Initiation of flowering (IF) 0.158 SD 0.78

Flower buds (FB) 0.143 PH 0.739

Panicle length (PL) 0.104 PM 0.724

Plant height (PH) 0.098 PL 0.705

Stem diameter (SD) 0.083 FB 0.68

Saponin content (SC) 0.078 PD 0.593

Harvest index (HI) 0.066 HI 0.522

Main branches (MB) 0.049 MB 0.5

Panicle diameter (PD) 0.047 TLM 0.396

Teeth on leaf margin (TLM) 0.036 SC 0.384

Emergence (E) 0.012 E 0.154




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Cluster Analysis

Through the k-means partition technique of the nonhierarchical procedure,

germplasm was grouped into seven clusters of different genetic diversity, each carrying

quinoa accessions sharing common properties and being highly similar to one another.

This clustering, combined with passport data, provided a useful overall description of the

germplasm. Only qualitative variables were included in this method.

Accessions in Cluster 1 characteristically had medium to large grains ð2:12 ^

0:14 mmÞ; with the highest saponin contents of the collection ð6:49 ^ 2:02 ccÞ; and were

relatively early maturing ð166 ^ 13 daysÞ: Plants had an intermediate architecture, usually

with a branching growth habit, and high harvest indexes. Amaranthiform panicles

prevailed over glomerulate panicles. Accessions from Cercado, Department of Oruro,

Bolivia, most represented the cluster.

Accessions in Cluster 2 characteristically had the largest grains of the collection

ð2:31 ^ 13 mmÞ; and were early maturing ð148 ^ 13 daysÞ: Whereas branching growth

habits were predominant, plant architecture was below the overall average for plant height,

stem diameter, and panicle length and diameter. Harvest indexes, however, were high. As

expected, amaranthiform panicles predominated within the cluster. The most

representative were those collected from the Salares (a region of salt-pans extending

across southern Oruro and northern Potosı), in Ladislao Cabrera, Department of Oruro,

and Nor Lıpez and Daniel Campos, Department of Potosı.

Accessions in Cluster 3 had high harvest indexes ð0:47 ^ 0:09Þ; small architecture

(plant height ¼ 95:06 ^ 11:62 cm; stem diameter ¼ 15:04 ^ 1:66 mm; simple growth

habits, i.e., few and short branches); and small- to medium-sized ð1:8 ^ 0:13 mmÞ grains,

with low saponin content ð1:38 ^ 2:27 ccÞ: The period of maturity was similar to that of

Cluster 1 ð168 ^ 14 daysÞ; but glomerulate panicles predominated. Most of the accessions

were collected in Aroma, Department of La Paz, and in several districts in the Department

of Puno, Peru. Surprisingly, the Chilean accessions were grouped in this cluster, perhaps

because the study did not consider discriminatory characters, as did Wilson (1988) in his

work with allozymes.

Accessions in Cluster 4 were tall ð119:17 ^ 9:45 cmÞ and moderately late maturing

ð184 ^ 10 daysÞ: Their grains were the smallest of the collection ð1:79 ^ 0:13 mmÞ; with

the lowest saponin contents ð0:97 ^ 1:46 ccÞ: Plants had few, short branches, and leaves

that were relatively less dentated. Panicles were longer than wide and were glomerulate.

This cluster contained accessions from areas surrounding Lake Titicaca and had the

highest percentage of Peruvian accessions.

Accessions in Cluster 5 were mostly late maturing ð196 ^ 7 daysÞ and had low harvest

indexes ð0:28 ^ 0:09Þ: Plants were tall, heavily branched, with thick stems and highly

dentated leaves; this last characteristic is common among quinoa accessions of valley

regions. Grains were medium-sized ð2 ^ 0:13 mmÞ; with high saponin contents ð5:39 ^

2:74 ccÞ: Panicles were wider than long—because of the plant’s open canopy—and

amaranthiform. The most representative quinoa accessions of this cluster come from the

highland valleys in the Bolivian departments of Potosı, Chuquisaca, Cochabamba, and

Tarija.

Accessions in Cluster 6 overall had the largest plant architectures of the collection

(i.e., plant height ¼ 128:99 ^ 13:4 cm; stem diameter ¼ 20:81 ^ 2:17 mm; panicle

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length ¼ 46:12 ^ 5:79 cm; panicle diameter ¼ 9:05 ^ 1:88 cm; and numerous branches).

These accessions, however, produced small- to medium-sized grains ð1:84 ^ 0:15 mmÞ;with low saponin contents, and were moderately late maturing ð188 ^ 11 daysÞ; similar to

Cluster 4. Glomerulate panicles predominated. As in Cluster 4, accessions from areas

surrounding Lake Titicaca most represented the cluster.

Cluster 7 contained the smallest number of accessions; these were the latest maturing

ð204 ^ 5 daysÞ; with the lowest harvest indexes ð0:19 ^ 0:08Þ: Plant architecture was

large, and plants were highly branched with highly dentated leaves ð24 ^ 6Þ; a

characteristic of quinoa accessions from valley regions (Risi and Galwey, 1989b).

Glomerulate panicles clearly predominated. Accessions from the lower altitude valleys of

the Cochabamba Department were the most representative.

Table 5 summarizes the profile of each cluster, indicating the broad variability of the

germplasm. Clusters are ordered according to variables that characterized the first

principal component. For example, quinoa accessions of Cluster 2 were the earliest

maturing and had high harvest indexes, and those of Cluster 7 were the latest maturing and

had low harvest indexes. Accessions of the other clusters (1, 3, 4, 5, and 6) had

intermediate growth cycles, with the harvest index decreasing as the maturity period

lengthened.

Quinoa accessions collected from areas around Lake Titicaca and in the central High

Plains of Bolivia (Clusters 3 and 4) had the fewest branches and the simplest growth

habits, corroborating Gandarillas’s (1968) findings and contrasting with the highly

branched accessions collected from valley regions (Clusters 5 and 7; Risi and Galwey,

1989a).

Table 5. Comparison profile of the seven clusters of quinoa accessions classified by the

k-means technique.

Clustera

Characteristics 2 1 3 4 6 5 7

Emergence (days) 12.4 12.5 13.1 13 14.7 13.0 14.2

Floral buds (days) 49.6 51 51.4 49.6 50.4 54.4 74.5

Initiation of flowering (days) 72.1 74.2 76.3 77.5 80.0 91.5 108.9

50% flowering (days) 84.5 88.3 89.3 90.2 92.9 106.9 134.8

Physiological maturity (days) 148.2 165.9 168.4 184.1 188.1 195.9 203.7

Harvest index (%) 47.1 47.1 47 40.2 40.1 27.7 19.2

Main branches (no.) 21.8 21 17.3 18 22.4 27.2 31.3

Teeth on leaf margins (no.) 15.1 14 12.7 12.6 14.1 17.8 24.3

Stem diameter (mm) 14.8 16.8 15 17.2 20.8 18.3 18.3

Panicle length (cm) 30.5 34.7 33.4 44.3 46.1 35.6 26.6

Panicle diameter (cm) 6 7.1 5.8 6.5 9.1 7.3 6.2

Plant height (cm) 93.3 104.8 95.1 119.2 129.0 119.1 121.3

Grain diameter (mm) 2.3 2.1 1.8 1.7 1.8 2 1.9

Weight of 100 grains (g) 0.4 0.3 0.2 0.2 0.2 0.3 0.3

Saponin content (cc) 3.4 6.5 1.4 0.9 2.0 5.4 4.0

Number of cases 221 218 234 355 182 254 48

a Clusters are ordered according to variables that characterized the first principal component.




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Accessions in Clusters 1 and 2 tend to have the largest grains, a characteristic of

accessions from the Salares. Germplasm of Clusters 3, 4, and 6, representing the areas

bordering Lake Titicaca and the Bolivian Central High Plains, have small- to medium-

sized grains, with low saponin contents (Table 5). The predominance of small-grain

accessions in this part of the High Plains was reported by Arze et al. (1977), when they

found that grain diameter of germplasm from Puno (Peru) ranged between 1.00 and

1.19 mm.

Multiple Discriminatory Analysis (MDA)

Quantitative variables were considered as independent and the clusters identified

by cluster analysis, as dependent variables. The discriminatory functions (Table 6)

differentiating among these clusters were obtained by the step-by-step procedure,

calculating on the basis of 15 independent variables that were significant in the

discriminatory model.

All discriminatory functions were statistically significant according to the chi-square

test at a probability of 0.001. Proper values and the distribution of their variances indicated

that the first two functions accounted for more than 80% of total variance. Wilks’ lambda

coefficients for these two functions were, precisely, the lowest, indicating an almost

perfect discrimination regarding the remaining functions. In contrast, the R 2 indicates the

percentage of variance explained by the model (Table 6).

Comparing the MDA with the PCA

The interpretation of independent variables was carried out with the potency index

(Hair et al., 1992), which measures the contribution of each variable, taking into account

all significant functions and, thus, the total discriminatory effect. The results obtained were

presented together with the degree of importance as determined by principal component

analysis (PCA) to compare the efficiency of both methods (Table 4).

In general, both methods (Table 4) determined that 50% flowering was the most

discriminatory variable and emergence the least. They also determined that grain diameter

Table 6. Discriminatory functions that distinguish between clusters of quinoa accessions.

ProperVariance (%)

Function value Function Cumulated R 2 coefficient Wilks’ l x2 df P

1 5.303 47.939 47.939 0.840 0.007 7460.4 90 0.001

2 3.553 32.123 80.062 0.780 0.043 4698.9 70 0.001

3 1.295 11.709 91.771 0.560 0.198 2425.3 52 0.001

4 0.399 3.611 95.382 0.280 0.456 1179.1 36 0.001

5 0.343 3.103 98.485 0.260 0.638 675.0 22 0.001

6 0.168 1.515 100 0.140 0.856 232.4 10 0.001

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and weight of 100 grains ranked third and fourth in importance. The specific position

reached by several variables, however, was not the same for the two methods. For

example, in the most notable cases, the MDA assigned greater importance to physiological

maturity, even more than to grain diameter and weight of 100 grains, whereas the PCA

allocated this variable to the seventh position. In contrast, the MDA notably improved the

position of saponin content, which was placed second last by the PCA.

Time to 50% flowering and physiological maturity were the most discriminatory

variables for cluster classification and were strongly dependent on genotype. Grain

diameter and weight of 100 grains likewise were highly discriminatory, and are dependent

on genotype, being highly inheritable (Espındola, 1980). Among the morphological traits,

panicle length, plant height, and stem diameter were the most important variables; these

form part of quinoa’s yield components.

To summarize, the results obtained through the MDA better reflected the performance

of variables, according to observations made during characterization and evaluation. In

contrast, the PCA assigns importance according to the correlations reached by the

variables in the similarity matrix. Both methods, however, complemented well in selecting

the most discriminatory variables.

Mahalanobis Distance

According to the Mahalanobis distance D 2 (Table 7), also calculated by

discriminatory analysis, the seven clusters were recognized as being statistically different

from each other. Clusters 2 and 7 were farther away on the matrix (D 2), with 112.89 units.

Cluster 7 grouped together the latest-maturing quinoa accessions, with areas of origin that

included the lower altitude valleys of Cochabamba (from 2558 to 3100 masl). Cluster 2, in

contrast, gathered together the earliest-maturing quinoa accessions, which came mainly

from the southern areas of the High Plains or from the Salares (from 3665 to 3700 masl).

The most similar clusters were, on the one hand, Clusters 4 and 6 (7.34 units) and, on

the other, Clusters 3 and 4 (7.81 units), indicating that the accessions classified in Cluster 4

shared several similar characteristics with Cluster 6 and several other characteristics with

Cluster 3. The three clusters gathered together quinoa accessions from the High Plains

shared by Peru and Bolivia.

Table 7. Mahalanobis distances (D 2) between seven clusters of quinoa germplasm.

Cluster 1 2 3 4 5 6 7

1 0.00

2 10.58** 0.00

3 13.23** 23.25** 0.00

4 18.89** 37.95** 7.81** 0.00

5 19.31** 43.62** 26.73** 19.26** 0.00

6 22.97** 50.23** 21.14** 7.34** 14.84** 0.00

7 86.04** 112.89** 90.28** 91.04** 47.88** 85.22** 0.00

** ¼ D 2, that is, distances differing from zero at a 99% confidence interval.




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Verifying the Predictive Ability of Discriminatory Functions

The classification matrix presented in Table 8 summarizes the predictive ability of

discriminatory functions when classifying the different groups of germplasm. According

to the column “Total number observed,” discriminatory analysis recognized, in each

group, the same number of accessions classified by the nonhierarchical procedure of

cluster analysis. However, discriminatory analysis is much more informative, because

misclassified accessions were identified and reassigned to the appropriate group. In

addition, the row “Total number predicted” indicates the true number of entries that should

be classified in each group.

In general, the discriminatory functions reached a high degree of precision for group

classification. In all cases, the scope surpassed 87% of correctly grouped accessions. The

degree of total precision was highly significant according to the “Q” statistical test (Hair

et al., 1992), indicating the high discriminatory ability of the classification matrix

(Table 8).

In Group 1, 204 of the 218 accessions were correctly classified (93.58%); the 14

misclassified accessions ð6 þ 4 þ 2 þ 2Þ corresponded, respectively, to Groups 2, 3, 4, and

5. In addition, 25 entries should be reassigned to add up to the 229 accessions predicted for

Group 1. In Group 2, 93.66% of the entries were correctly classified. Among the

accessions misclassified, 12 corresponded to Group 1 and only 2 accessions to Group 3.

Six should be reassigned from Group 1 to add up to the 213 accessions predicted. The

same procedure of interpretation should be performed for Groups 3, 4, 5, 6, and 7 (Table 8).

To have a comprehensive perspective of the diversity of the germplasm under study,

Fig. 1 shows how all accessions are classified in the seven groups according to the first two

discriminatory functions. The first function separated Groups 1, 2, and 3 clearly from

Groups 4, 5, 6, and 7. For example, among the groups farthest away from this function,

Group 2 was the earliest maturing, with high harvest indexes and small plants. In contrast,

the accessions of Group 7 were the latest maturing of all the germplasm in the collection,

with the lowest harvest indexes and big plants. The other groups occupied intermediate

positions, reflecting sufficient variability for these characteristics.

Table 8. Classification matrix of seven groups of quinoa germplasm.

Group

Correct

percent 1 2 3 4 5 6 7

Total

number

observed

1 93.58 204 6 4 2 2 0 0 218

2 93.66 12 207 2 0 0 0 0 221

3 88.46 8 0 207 17 2 0 0 234

4 92.39 0 0 14 328 2 11 0 355

5 95.28 2 0 0 1 242 8 1 254

6 91.76 3 0 1 6 5 167 0 182

7 87.5 0 0 0 0 6 0 42 48

Total number

predicted

92.39 229 213 228 354 259 186 43 1512

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The second discriminatory function distinctly separated Groups 3, 4, and 6 from

Groups 1, 2, 5, and 7. Accessions in the first set of groups were small- to medium-seeded,

with low saponin content and long panicles. In the second set of groups, accessions were

characterized by medium to large grains, with high saponin content, and short panicles

(Fig. 1).

Three areas of genetic diversity can be readily defined according to altitude: 1) the

lower altitude valleys, to which Group 7 belongs (from 2558 to 3000 masl); 2) the High

Plains (from 3665 to 3750 masl), which includes most of the groups (1, 2, 3, 4, and 6); and

3) the higher altitude valleys (from 3000 to 3500 masl), to which Group 5 belongs and

which represents a transitional zone between the lower altitude valleys and the High Plains

(Fig. 2).

In the High Plains, members of Group 2, which represents the accessions from the

Salares, are found farthest south. These accessions are the earliest maturing, not only of the

Andean region, but also of the entire germplasm collection. Accessions of Group 6 were,

in contrast, the latest maturing and were found far north. Accordingly, the maturity period

of these quinoa accessions gradually varied according to latitude of origin. Groups 5 and 7

are even more late maturing but for reasons of altitude, not latitude.

The 12 quinoa accessions from southern Chile included in the survey were expected to

fall within the group of sea-level accessions (Lescano, 1989; Tapia, 1990). This, however,

did not occur, because the traits considered were not sufficiently discriminatory to classify

the accessions individually as was done by Wilson (1988), using allozymes and describing

in detail the leaf-blade surface.

Most quinoa production is found in the Bolivian High Plains, which are usually

divided into three regions: the northern High Plains, represented by the most predominant

Bolivian quinoa accessions of Groups 4 and 6; the central High Plains, mainly represented

by Group 3; and the southern High Plains, represented by Group 2. However, the limit

between the central and southern High Plains is not well defined and is thus controversial,

Figure 1. Graphic illustration of the discriminatory analysis of seven similarity groups of quinoa

germplasm.




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the reason being that, between these two regions, a well-defined intermediate area of

quinoa diversity, represented by Group 1 (Fig. 2), can be found. The Bolivian High Plains,

therefore, has four production areas, not the three usually considered.

More research on the location of geographic centers is needed. The data in this study

were determined only on the basis of passport data of those accessions found closest to the

centers of gravity. A geographic analysis should be conducted, based on collection data,

followed by analysis ofthe taxonomic correspondence.

ACKNOWLEDGMENTS

To Luigi Guarino of IPGRI for his collaboration in handling the translation of the

present article.

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Figure 2. Location of centers of gravity (centroids) of the seven groups of quinoa germplasm

classified by discriminatory functions.

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Multivariate Analysis of Genetic Diversity of Bolivian Quinoa Germplasm

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